Proof: Linear Combination of X0 and X1

[vg19]

Im not too sure on where to start on this proof. Any hints would be very helpful.

If X0 and X1 are solutions to the homogeneous system of equations AX=0, show that sX0 + tX1 is also a solution for any scalars s and t (called a linear combination of X0 and X1)

 

[TD]

First off, a homogeneous system always has at least 1 solution, namely the zero-solution. So if the system has a unique solution, it has to be that one. If you find another one besides that though, you immediately have infinite solutions.

Since X0 and X1 are solutions, you know that A(X0) = 0 and A(X1) = 0.
Now, what do you know about A(sX0+tX1), try simplifying that expression so you can use what you are given.